Limited Maze Solver With DifferentialPilot and PIDController

Maze solver being a complex topic for me, I decided to start with a simplest maze first (check the video). The program is inspired by the video here. The main reference for finding the shortest path is here. The code for this program is given below. The program works with DifferentialPilot and PIDController classes supported by leJOS. The program works in two phases. In the first phase, it samples the entire path for the direction in which the robot is moving. It then applies the shortest path algorithm over the direction. In the second phase robot follows the shortest path. I will explain all the methods in the program below. 

Cruiser(): This is the Cruiser class constructor which internally calls pidInitialize(), pilotInitialize(), pid1Initialize(), pilot1Initialize(). 

run(): This is the method over the Cruiser thread which implements the shortest path following algorithm (from the left), by calling following methods in sequence:

• populateFirstPathSamples()
• findShortedPath()
• followShortestPath()

populateFirstPathSamples(): It populates the summary array. This array contains the instantaneous values of X and Y coordinate of the robot's pose and also the Direction of the robot's pose while traversing the path for the first time. I have introduced a variable removal in order to use it for plotting the trajectory of the shortest path. This method executes the following steps in order to populate the summary array:

• Call getASample(), which return the X and Y coordinates for the robot, based on its pose while collecting the sample
• Populate X, Y, Direction and Removal properties for the sample in a Direction object and create a single entry in the summary array. Please note that the Direction object has a direction property too. 
• Repeat the above steps for 180 times (The figure 180 samples collection, is coined through a bit of trial and error). You guessed it right, there will be 180 entries in the summary array at the end of the traversing the entire path for the first time. Each entry will be of type Direction object 

getASample(): Steers the entire path with the PID controller and samples the path after each 10 milli seconds. It does such sampling 10 times, gets the X and Y position at each sample. It averages X and Y over these 10 samples. It puts the X and Y values in the sample array. So, by this time you should know that each sample consists of only 2 elements, the X and Y coordinates of robot's pose (averaged over 10 samples). 

getDirection(): This method decides the direction in which the robot is moving as per the following figure. 

This method assigns the following numbers with the directions:

North = 1

East = 2

South = 3

West = 4

Below is the algorithm for setting up the direction variable

• The input to this method is the X and Y coordinates of the current pose and its previous pose. 
• dx is difference between the X coordinate of the current pose and X coordinate of previous pose
• dy is the difference between Y coordinate of current pose and Y coordinate of previous pose
• I have set direction of movement from South to North to be when the line passing through the two poses of the robot has a slope less than 1 and dx is greater than 0
• I have set direction of movement from North to South to be when the line passing through the two poses of the robot has a slope less than 1 and dx is less than 0
• I have set direction of movement from East to West to be when the line passing through the two poses of the robot has a slope greater than 1 and dy is greater than 0
• I have set direction of movement from West to East to be when the line passing through the two poses of the robot has a slope greater than 1 and dy is less than 0

summarize(): This method executes the following crucial steps:

• Out of 180 summary samples, remove all the summary samples where direction = 0. That means neither of East, West, North, South is associated with it
• Out of the remaining summary samples, consider only those where consecutive samples does NOT have the same direction. That means I am considering only those consecutive summary elements with changes in the direction to be on the shortest path. 

findShortedPath(): As mentioned in the summarize() method above, the shortest path list takes all the summary samples which represent change in the direction, as an input. Then it removes all the samples where the previous three direction changes look like 4-1-2 in a sequence corresponding to West-North-East. This sequence represent the U turn (which is little delayed turn) which the robot takes at the dead end. I have come up with this sequence removal after observing the logs which I print in the program. 

followShortestPath(): As we know now, that the shortest path constitutes the changes in the direction of the robot. To follow the path, consider the following algorithm. 

• Collect the first three samples from pilot1 for the second phase. 
• Don't take any action until the three samples are aligned in the same direction as shortest path. Just keep following the path. 
• The moment the direction of the three samples get misaligned, start taking a turn. Then stabilize until the stabilization count gets decremented to zero. 
• After mis-aligning and consequent stabilization, if the three consecutive samples get aligned with the next index of the shortest path, increment the shortest path index to point to the next direction.
• Then start with the next three samples of pilot1 and repeat the same procedure again!   

NOTE: The number three for three consecutive samples while following the shortest path is considered after some trial and error. We can even go for comparing two samples or four samples. However, two samples will make the algorithm more error prone. And four samples will create some delay in processing.  

Line Follower with LeJOS DifferentialPilot and PIDController classes

Below is the program which makes use of LeJOS DifferentialPilot and PIDController classes to make a line follower. The underlying PID Controller concept is the same as explained in the article Line Follower with PID Controller. The appropriate values of Kp, Ki and Kd are set in the program. Higher values of Ki makes the robot unstable in line following (makes it go round and round around itself). Lower values of Kd gives a delayed response when following sharp runs (like a right/left/U turn). Higher values of Kp makes the robot follow the line in a shaky manner. The video clip shows the performance of the program.

Let me explain the Cruiser class of the LeJOS program below. The core classes, their attributes and methods used in the Cruiser class are explained in the LeJOS APIs at the below links:

• DifferentialPilot
• OdometryPoseProvider
• PIDController

The program starts with setting the parameters - wheel diameter, track width, left motor, right motor and reverse setting which are required for DifferentialPilot to function. The OdometryPoseProvider is then initialized with DifferentialPilot class object passed to its constructor, in order to track the pose of the robot in the 2D-space. The pose represents the current location and the heading of the robot. For the pose, the distance travelled by the robot is measured in Pilot units (that means if we have set the wheel diameter and track width in inches, we will get the distance travelled in inches. If we have set them in centimeters, we will get the distance in centimeters). The heading angle is measured in degrees. The pose readings are required if we want to plot the trajectory of the robot. An example of expected trajectory is given below. 

     

After feeding the instantaneous pose readings into a graph plotter (like plotly), we get to see the actual trajectory as follows:

To take a look at good in-place U-Turns at the dead ends, please take a look at below video. 

In our example of Line Follower, the pose readings do not exactly match with the actuals after the robot performs U-turns at the dead-ends. If we apply certain correction for in-place U-Turns, we may be able to get the exact trajectory. However, I have not applied any correction for this plot but we do get an idea of the trajectory that the robot is following. More concrete use of the pose, will be explained in the Maze Solver article. For now, in the Cruiser, we need to set the travel speed and the rotate speed of the robot. Travel speed is in the wheel-diameter unit per second and the rotate speed is in degrees per second. Further, we initialize the PIDController constructor with the set-point (in our case, the threshold value), set the required PID parameters and pass the instantaneous value of the light intensity to the doPID () method. The Kp, Ki and Kd needs to be tuned appropriately in order for the robot to follow the black line over white surface. 

NOTE: It would serve great help if you read the below article before going through code given in current article. That will make you familiar with the calibration concept. 

Line Follower with PID Controller

Line Follower with PID Controller

I am sharing the leJOS line follower program with PID controller. Here is the reference literature for PID controller. As we all know the PID Controller works based on continuous feedback from the system relative to a given set-point. If the system moves away from the set-point, the feedback is provided such that, it will return back to the set-point. The PID algorithm works so as to minimize the error between the actual and the set-point. In case of the Line-Follower program below, the system is the Line-Follower itself. The set-point is the light intensity which the system has to follow in order to continue moving on the black line and should not lose the track. In our case, we define the set-point as the average light intensity of black and white colors. We call the set-point as threshold. The way of configuring the threshold being average = (black + white)/2, the line-follower follows the edge of the black stripe placed on the white paper. I have put two perpendicular stripes for the line follower as a challenge, to know how precisely it can follow the turn. (It is relatively easy for the line follower to follow smooth curves. But most of the time in real-life scenario, we do not get smooth turns. We encounter perpendicular sharp turns). The other challenge was to find out how effectively the line-follower faces a dead-end. Hence in the below small experiment, I have incorporated two perpendicular turns and two dead-ends with black stripes. You can imagine it as a road, on which the car is moving with a relatively slow speed. The speed is kept slow in order for the Line-Follower not to lose its track. We can even increase the speed and try the same experiment, but let us keep that for some other time. 

Now let us look at the digitized-PID controller algorithm which I have incorporated in the LeJOS program below. The set-point is the threshold as described in the above paragraph. The feedback is provided in the form of error, which is the difference between the actual-light-intensity at any given instance and the threshold value. If the actual-light-intensity of the robot is more towards black or more towards white, the system will pull it back towards the threshold, i.e. the edge of the line. In the below digitized-PID algorithm, we convert the error, its integral and its derivative into power value which will be supplied to the right and left motors. The power will be supplied to the motors such that, if the car is too much on the black surface, it will be pulled on to the white surface and vice-versa. In the digitized version of the integral error, the past error value is added to the current error value iteratively. While the digitized version of derivative, the last error is subtracted from the current error iteratively. Please take a look into the following three lines of code for illustration, where color represents the current light intensity based on the robot's position on the black or white surface.

  

The correction variable represents the calculated value of power, where error term gets multiplied by Kp (the proportional coefficient), the integral term gets multiplied by Ki (the integral coefficient) and the derivative term gets multiplied by Kd (the derivative coefficient). The Kp, Ki and Kd need to be tuned in order for the Line-Follower to follow the line appropriately with a certain speed. In my case the default power of the Line-Follower is set to 20. This value is based on trial and error in order for the speed to be relatively slow. Below is the video clip to show the performance of the program for given kp, ki and kd parameters.  

NOTE - In order for the Calibration details of Black and White intensities, it would better to take a look at my Line Follower program first.

Observations: The program seems to be following the perpendicular turn well with the current Kp, Kd and Ki coefficients and the given speed. However, it does not take the U turn at the dead-end very well. For taking an in-place U turn there is a need for more fine-tuning of PID coefficients. To know about how a better in-place U-turn looks like, please take a look at my video In-Place U turn. I have not yet concluded anything about the 'effect of tuning the parameters' over the line follower. However, that would be reserved for the future. 

I hope you liked this article!